European political fears shook the markets Monday, sending the broad S&P sliding 1.2% in its steepest drop since November. However, a round of better-than-expected data lifted sentiment Tuesday.

A final reading of Markit's eurozone composite PMI gauge checked in at 48.6 in January from a previous estimate of 48.2 and 47.2 in December. It suggests the 17-member currency bloc's economy is still shrinking, but at its slowest pace in 10 months as declines were slowed in both the manufacturing and services components.

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"The eurozone is showing clear signs of healing, with the downturn easing sharply in January and the region moving closer to stabilisation in the first quarter," Markit Chief Economist Chris Williamson said in the report.

Still, the recovery hasn't been spread evenly. Germany's economy, Europe's biggest, is growing, while France, Italy and Spain are still pulling back.

A separate PMI report from HSBC showed output across China's manufacturing and services sectors heated up at the swiftest pace in two years. The data have helped to ease fears that the economy could be in for a so-called "hard landing" in which the rate of growth plunges.

Later in the day, traders will get a fresh look at how the U.S. services sector fared in January. Economists expect the key component of the world's biggest economy to have expanded at a slightly slower pace than it did in the previous month.

Analysts also noted attention could shift back to Capitol Hill as the Congressional Budget Office is set to release its annual budget and economic outlook. The debt ceiling has been temporarily suspended until May 18, but there is still expected to be haggling over that measure, and sequestration, which goes into effect in March.